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                                                                     EXHIBIT 4.2

                                     FORM OF
                           CERTIFICATE OF DESIGNATION

                                       of

                  SERIES A JUNIOR PARTICIPATING PREFERRED STOCK

                                       of

                         THE HOUSTON EXPLORATION COMPANY

             Pursuant to Section 151 of the General Corporation Law
                            of the State of Delaware

         The Houston Exploration Company, a corporation organized and existing
under the General Corporation Law of the State of Delaware (the "Corporation"),
in accordance with the provisions of Section 103 thereof, DOES HEREBY CERTIFY:

         That pursuant to the authority vested in the Board of Directors of the
Corporation (the "Board of Directors") in accordance with the provisions of the
Restated Certificate of Incorporation of the said Corporation, the said Board of
Directors on August 12, 2004 adopted the following resolution creating a series
of 400,000 shares of Preferred Stock designated as "Series A Junior
Participating Preferred Stock":

                  RESOLVED, that pursuant to the authority vested in the Board
         of Directors of this Corporation in accordance with the provisions of
         the Restated Certificate of Incorporation, a series of Preferred Stock,
         par value $0.01 per share, of the Corporation be and hereby is created,
         and that the designation and number of shares thereof and the voting
         and other powers, preferences and relative, participating, optional or
         other rights of the shares of such series and the qualifications,
         limitations and restrictions thereof are as follows:

                  SERIES A JUNIOR PARTICIPATING PREFERRED STOCK

         1. Designation and Amount. There shall be a series of Preferred Stock
that shall be designated as "Series A Junior Participating Preferred Stock," and
the number of shares constituting such series shall be 400,000. Such number of
shares may be increased or decreased by resolution of the Board of Directors;
provided, however, that no decrease shall reduce the number of shares of Series
A Junior Participating Preferred Stock to less than the number of shares then
issued and outstanding plus the number of shares issuable upon exercise of
outstanding rights, options or warrants or upon conversion of outstanding
securities issued by the Corporation.


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         2. Dividends and Distribution.

                  (A) Subject to the prior and superior rights of the holders of
any shares of any class or series of stock of the Corporation ranking prior and
superior to the shares of Series A Junior Participating Preferred Stock with
respect to dividends, the holders of shares of Series A Junior Participating
Preferred Stock, in preference to the holders of shares of any class or series
of stock of the Corporation ranking junior to the Series A Junior Participating
Preferred Stock in respect thereof, shall be entitled to receive, when, as and
if declared by the Board of Directors out of funds legally available for the
purpose, quarterly dividends payable in cash on the final day of March, June,
September and December, in each year (each such date being referred to herein as
a "Quarterly Dividend Payment Date"), commencing on the first Quarterly Dividend
Payment Date after the first issuance of a share or fraction of a share of
Series A Junior Participating Preferred Stock, in an amount per share (rounded
to the nearest cent) equal to the greater of (a) $10.00 or (b) the Adjustment
Number (as defined below) times the aggregate per share amount of all cash
dividends, and the Adjustment Number times the aggregate per share amount
(payable in kind) of all non-cash dividends or other distributions other than a
dividend payable in shares of Common Stock or a subdivision of the outstanding
shares of Common Stock (by reclassification or otherwise), declared on the
Common Stock, par value $0.01 per share, of the Corporation (the "Common Stock")
since the immediately preceding Quarterly Dividend Payment Date, or, with
respect to the first Quarterly Dividend Payment Date, since the first issuance
of any share or fraction of a share of Series A Junior Participating Preferred
Stock. The "Adjustment Number" shall initially be 1000. In the event the
Corporation shall at any time after August 23, 2004 (i) declare and pay any
dividend on Common Stock payable in shares of Common Stock, (ii) subdivide the
outstanding Common Stock or (iii) combine the outstanding Common Stock into a
smaller number of shares, then in each such case the Adjustment Number in effect
immediately prior to such event shall be adjusted by multiplying such Adjustment
Number by a fraction the numerator of which is the number of shares of Common
Stock outstanding immediately after such event and the denominator of which is
the number of shares of Common Stock that were outstanding immediately prior to
such event.

                  (B) The Corporation shall declare a dividend or distribution
on the Series A Junior Participating Preferred Stock as provided in paragraph
(A) above immediately after it declares a dividend or distribution on the Common
Stock (other than a dividend payable in shares of Common Stock).

                  (C) Dividends shall begin to accrue and be cumulative on
outstanding shares of Series A Junior Participating Preferred Stock from the
Quarterly Dividend Payment Date next preceding the date of issue of such shares
of Series A Junior Participating Preferred Stock, unless the date of issue of
such shares is prior to the record date for the first Quarterly Dividend Payment
Date, in which case dividends on such shares shall begin to accrue from the date
of issue of such shares, or unless the date of issue is a Quarterly Dividend
Payment Date or is a date after the record date for the determination of holders
of shares of Series A Junior Participating Preferred Stock entitled to receive a
quarterly dividend and before such Quarterly Dividend Payment Date, in either of
which events such dividends shall begin to accrue and be cumulative from such
Quarterly Dividend Payment Date. Accrued but unpaid dividends shall not bear
interest. Dividends paid on the shares of Series A Junior Participating
Preferred Stock



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in an amount less than the total amount of such dividends at the time accrued
and payable on such shares shall be allocated pro rata on a share-by-share basis
among all such shares at the time outstanding. The Board of Directors may fix a
record date for the determination of holders of shares of Series A Junior
Participating Preferred Stock entitled to receive payment of a dividend or
distribution declared thereon, which record date shall be no more than 60 days
prior to the date fixed for the payment thereof.

         3. Voting Rights. The holders of shares of Series A Junior
Participating Preferred Stock shall have the following voting rights:

                  (A) Each share of Series A Junior Participating Preferred
Stock shall entitle the holder thereof to a number of votes equal to the
Adjustment Number on all matters submitted to a vote of the stockholders of the
Corporation.

                  (B) Except as required by law, by Section 3(C) and by Section
10 hereof, holders of Series A Junior Participating Preferred Stock shall have
no special voting rights and their consent shall not be required (except to the
extent they are entitled to vote with holders of Common Stock as set forth
herein) for taking any corporate action.

                  (C) If, at the time of any annual meeting of stockholders for
the election of directors, the equivalent of six quarterly dividends (whether or
not consecutive) payable on any share or shares of Series A Junior Participating
Preferred Stock are in default, the number of directors constituting the Board
of Directors of the Corporation shall be increased by two. In addition to voting
together with the holders of Common Stock for the election of other directors of
the Corporation, the holders of record of the Series A Junior Participating
Preferred Stock, voting separately as a class to the exclusion of the holders of
Common Stock, shall be entitled at said meeting of stockholders (and at each
subsequent annual meeting of stockholders), unless all dividends in arrears on
the Series A Junior Participating Preferred Stock have been paid or declared and
set apart for payment prior thereto, to vote for the election of two directors
of the Corporation, the holders of any Series A Junior Participating Preferred
Stock being entitled to cast a number of votes per share of Series A Junior
Participating Preferred Stock as is specified in paragraph (A) of this Section
3. Until the default in payments of all dividends which permitted the election
of said directors shall cease to exist, any director who shall have been so
elected pursuant to the provisions of this Section 3(C) may be removed at any
time, without cause, only by the affirmative vote of the holders of the shares
of Series A Junior Participating Preferred Stock at the time entitled to cast a
majority of the votes entitled to be cast for the election of any such director
at a special meeting of such holders called for that purpose, and any vacancy
thereby created may be filled by the vote of such holders. If and when such
default shall cease to exist, the holders of the Series A Junior Participating
Preferred Stock shall be divested of the foregoing special voting rights,
subject to revesting in the event of each and every subsequent like default in
payments of dividends. Upon the termination of the foregoing special voting
rights, the terms of office of all persons who may have been elected directors
pursuant to said special voting rights shall forthwith terminate, and the number
of directors constituting the Board of Directors shall be reduced by two. The
voting rights granted by this Section 3(C) shall be in addition to any other
voting rights granted to the holders of the Series A Junior Participating
Preferred Stock in this Section 3.



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         4. Certain Restrictions.

                  (A) Whenever quarterly dividends or other dividends or
distributions payable on the Series A Junior Participating Preferred Stock as
provided in Section 2 are in arrears, thereafter and until all accrued and
unpaid dividends and distributions, whether or not declared, on shares of Series
A Junior Participating Preferred Stock outstanding shall have been paid in full,
the Corporation shall not:

                           (i) declare or pay dividends on, make any other
distributions on, or redeem or purchase or otherwise acquire for consideration
any shares of stock ranking junior (either as to dividends or upon liquidation,
dissolution or winding up) to the Series A Junior Participating Preferred Stock;

                           (ii) declare or pay dividends on or make any other
distributions on any shares of stock ranking on a parity (either as to dividends
or upon liquidation, dissolution or winding up) with the Series A Junior
Participating Preferred Stock, except dividends paid ratably on the Series A
Junior Participating Preferred Stock and all such parity stock on which
dividends are payable or in arrears in proportion to the total amounts to which
the holders of all such shares are then entitled; or

                           (iii) purchase or otherwise acquire for consideration
any shares of Series A Junior Participating Preferred Stock, or any shares of
stock ranking on a parity with the Series A Junior Participating Preferred
Stock, except in accordance with a purchase offer made in writing or by
publication (as determined by the Board of Directors) to all holders of Series A
Junior Participating Preferred Stock, or to such holders and holders of any such
shares ranking on a parity therewith, upon such terms as the Board of Directors,
after consideration of the respective annual dividend rates and other relative
rights and preferences of the respective series and classes, shall determine in
good faith will result in fair and equitable treatment among the respective
series or classes.

                  (B) The Corporation shall not permit any subsidiary of the
Corporation to purchase or otherwise acquire for consideration any shares of
stock of the Corporation unless the Corporation could, under paragraph (A) of
this Section 4, purchase or otherwise acquire such shares at such time and in
such manner.

         5. Reacquired Shares. Any shares of Series A Junior Participating
Preferred Stock purchased or otherwise acquired by the Corporation in any manner
whatsoever shall be retired promptly after the acquisition thereof. All such
shares shall upon their retirement become authorized but unissued shares of
Preferred Stock and may be reissued as part of a new series of Preferred Stock
to be created by resolution or resolutions of the Board of Directors, subject to
any conditions and restrictions on issuance set forth herein.

         6. Liquidation, Dissolution or Winding Up. (A) Upon any liquidation,
dissolution or winding up of the Corporation, voluntary or otherwise, no
distribution shall be made to the holders of shares of stock ranking junior
(either as to dividends or upon liquidation,



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dissolution or winding up) to the Series A Junior Participating Preferred Stock
unless, prior thereto, the holders of shares of Series A Junior Participating
Preferred Stock shall have received an amount per share (the "Series A
Liquidation Preference") equal to the greater of (i) $10.00 plus an amount equal
to accrued and unpaid dividends and distributions thereon, whether or not
declared, to the date of such payment, or (ii) the Adjustment Number times the
per share amount of all cash and other property to be distributed in respect of
the Common Stock upon such liquidation, dissolution or winding up of the
Corporation.

                  (B) In the event, however, that there are not sufficient
assets available to permit payment in full of the Series A Liquidation
Preference and the liquidation preferences of all other classes and series of
stock of the Corporation, if any, that rank on a parity with the Series A Junior
Participating Preferred Stock in respect thereof, then the assets available for
such distribution shall be distributed ratably to the holders of the Series A
Junior Participating Preferred Stock and the holders of such parity shares in
proportion to their respective liquidation preferences.

                  (C) Neither the merger or consolidation of the Corporation
into or with another entity nor the merger or consolidation of any other entity
into or with the Corporation shall be deemed to be a liquidation, dissolution or
winding up of the Corporation within the meaning of this Section 6.

         7. Consolidation, Merger, Etc. In case the Corporation shall enter into
any consolidation, merger, combination or other transaction in which the
outstanding shares of Common Stock are exchanged for or changed into other stock
or securities, cash and/or any other property, then in any such case each share
of Series A Junior Participating Preferred Stock shall at the same time be
similarly exchanged or changed in an amount per share equal to the Adjustment
Number times the aggregate amount of stock, securities, cash and/or any other
property (payable in kind), as the case may be, into which or for which each
share of Common Stock is changed or exchanged.

         8. No Redemption. Shares of Series A Junior Participating Preferred
Stock shall not be subject to redemption by the Corporation.

         9. Ranking. The Series A Junior Participating Preferred Stock shall
rank junior to all other series of the Preferred Stock as to the payment of
dividends and as to the distribution of assets upon liquidation, dissolution or
winding up, unless the terms of any such series shall provide otherwise, and
shall rank senior to the Common Stock as to such matters.

         10. Amendment. At any time that any shares of Series A Junior
Participating Preferred Stock are outstanding, the Certificate of Incorporation
of the Corporation shall not be amended, by merger, consolidation or otherwise,
which would materially alter or change the powers, preferences or special rights
of the Series A Junior Participating Preferred Stock so as to affect them
adversely without the affirmative vote of the holders of two-thirds of the
outstanding shares of Series A Junior Participating Preferred Stock, voting
separately as a class.



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         11. Fractional Shares. Series A Junior Participating Preferred Stock
may be issued in fractions of a share that shall entitle the holder, in
proportion to such holder's fractional shares, to exercise voting rights,
receive dividends, and participate in distributions and to have the benefit of
all other rights of holders of Series A Junior Participating Preferred Stock.

         IN WITNESS WHEREOF, the undersigned has executed this Certificate this
__th day of August, 2004.

                                         THE HOUSTON EXPLORATION COMPANY



                                         By:
                                            ------------------------------------
                                            Name:
                                            Title:



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